The March, 2018 issue of the US Naval Institute Proceedings has an article by Commanders Timothy Kerze and Dana Brooke Reid, USCG, that advocates reinstating the Coast Guard’s ASW mission.
Specifically they suggest that the ten National Security Cutters (NSC) and 25 Offshore Patrol Cutters (OPC) be equipped and configured to operate the MH-60R in the ASW role. They contend that all 35 ships in the program of record could be so equipped for $122.5M, far less than the cost of a single Navy frigate.
They also refer briefly to the possibility of adding a sonar. I feel adding a long range detection capability would be a necessity. The ASW helicopters would be much more useful if the cutters could provide an around the clock cueing. Even adding this capability, perhaps in the form of LCS ASW module components to be manned by Navy Reservists when the need arises, would still likely keep the total cost of the program less than that of a single FFG, now expected to cost $800M.
As for employment, surface ships patrolling for submarines has never been very effective. Escorting other ships has always been the most effective tactic for countering submarines, because it draws the submarines to the escorts and because the subs must frequently abandon their most stealthy mode of operation to make an attack. ASW equipped cutters could be assigned to escort duties in areas away from the enemy’s air and surface threats.